The Cardiovascular System: Mathematical Modeling, Numerical Algorithms, Clinical Applications

38/2016

The Cardiovascular System: Mathematical Modeling, Numerical Algorithms, Clinical Applications

Monday 7th November 2016

Quarteroni, A.; Manzoni, A.; Vergara, C.

Mathematical and numerical modeling of the cardiovascular system is a research topic that has attracted a remarkable interest from the mathematical community because of the intrinsic mathematical difficulty and due to the increasing impact of cardiovascular diseases worldwide. In this review article, we will address the two principle components of the cardiovascular system, the arterial circulation and the heart function. We systematically go through the complete pipeline from data imaging acquisition, setting the basic physical principles, analyzing the associated mathematical models that comprise PDEs and ODEs systems, proposing sound and efficient numerical methods for their approximation, simulating both benchmark problems and clinically inspired (driven) problems. Mathematical modeling itself features tremendous challenges, due to the amazing complexity of the cardiocirculatory system, the multiscale nature of the involved physiological processes, and the need of devising computational methods that are stable, reliable, and efficient. A critical issue is about filtering the data, identifying the parameters of mathematical models, devising optimal treatments, accounting for uncertainties. For this reason, we will devote the last part of the paper to control and inverse problems, including parameter estimation, uncertainty quantification and the development of reduced order models that are of paramount importance when solving problems with high complexity, that would be out of reach otherwise.